Dehomogenization for completely positive tensors

Jiawang Nie; Xindong Tang; Zi Yang; Suhan Zhong

doi:10.3934/naco.2022037

Dehomogenization for completely positive tensors

Jiawang Nie, Xindong Tang, Zi Yang, Suhan Zhong^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

1 Citation (Scopus)

Abstract

A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations for CP tensors. Detection for CP tensors and the linear conic optimization with CP tensor cones can be solved more efficiently by the dehomogenization approach.

Original language	English
Pages (from-to)	340-363
Number of pages	24
Journal	Numerical Algebra, Control and Optimization
Volume	13
Issue number	2
Early online date	1 Jan 2023
DOIs	https://doi.org/10.3934/naco.2022037
Publication status	Published - Jun 2023

User-Defined Keywords

Tensor
complete positivity
dehomogenization
moment
semidefinite relaxation

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10.3934/naco.2022037

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abstract = "A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations for CP tensors. Detection for CP tensors and the linear conic optimization with CP tensor cones can be solved more efficiently by the dehomogenization approach.",

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AU - Nie, Jiawang

AU - Tang, Xindong

AU - Yang, Zi

AU - Zhong, Suhan

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N2 - A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations for CP tensors. Detection for CP tensors and the linear conic optimization with CP tensor cones can be solved more efficiently by the dehomogenization approach.

AB - A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations for CP tensors. Detection for CP tensors and the linear conic optimization with CP tensor cones can be solved more efficiently by the dehomogenization approach.

KW - Tensor

KW - complete positivity

KW - dehomogenization

KW - moment

KW - semidefinite relaxation

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DO - 10.3934/naco.2022037

M3 - Journal article

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EP - 363

JO - Numerical Algebra, Control and Optimization

JF - Numerical Algebra, Control and Optimization

IS - 2

ER -

Dehomogenization for completely positive tensors

Abstract

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